Question

The product of two proper fractions is ________ than each of the fractions that are multiplied.

Answer 1

Hint: Before we can solve this type of question, we must first understand the notion of faction and then appropriate fraction. Then to answer this question we need to consider the example and by further solving this example we get the answer.

Complete step-by-step solution:
Before going to this type of problem, first of all we need to understand the concept of fraction.
The concept of fractions is useful in our day-to-day life. For example, if you divide an apple into 4 equal parts then the value of each part is $${\displaystyle \frac{1}{4}}$$ and if you divide by 8 into equal parts then the value of each part is $${\displaystyle \frac{1}{8}}$$ .
Fraction multiplication is the same as multiplication of numbers in the number system. A fraction is a representation of how a whole is divided. When a fraction is multiplied by a whole number, the result can be either a fraction or a whole number. When multiplied by a variable, however, it becomes a variable quantity. It has both a numerator and a denominator.
There are many types of fractions like improper, proper and fixed fraction.
Out of these we will discuss the proper fraction only. Because the concept of proper fraction will be required to solve this above question.
Concept of proper fraction: A fraction in which the numerator (the upper value) is less than the denominator that is $$\text{numerator}<\text{denominator}$$. For example- $${\displaystyle \frac{4}{5}}$$, $${\displaystyle \frac{2}{4}}$$ is a proper fraction because here you can see that the numerator is less than the denominator.
Now, we come to the question
Here, it is asked related to the product of proper fraction.
To solve this type of question we always need to consider example that means
 Consider the proper fraction first, that is $${\displaystyle \frac{4}{5}}$$ and $${\displaystyle \frac{2}{4}}$$
We have to multiply this two-proper fraction that is
$$={\displaystyle \frac{4}{5}}\times {\displaystyle \frac{2}{4}}$$
By simplifying further, we get:
$$={\displaystyle \frac{2}{5}}$$
By reducing this proper fraction, we get:
$$=0.4$$
That means 0.4 is multiplied to the proper fraction is less than each of the fractions that are multiplied $$={\displaystyle \frac{4}{5}}\times 0.4=0.32$$.
Hence, we can say that the product of two proper fractions is less than each of the fractions that are multiplied.

Note: Always note that the value of proper fraction after simplification is less than 1. Most of the students can make mistakes by identifying the proper fraction hence, the concept of proper fraction should be clear. To attempt this type of question, always consider an example , then it is easier to understand the problem and we can solve it easily to get the answer.